Eduard M. Pittich

New catalogue of one-apparition comets discovered in the years 1901–1950 - I. Comets from the Oort spike

Context. The orbits of one-apparition comets discovered in the early part of the last century have formerly been determined with very different numerical methods and assumptions on the model of the solar system, including the number of planets taken into account. Moreover, observations of the comet-minus-star-type sometimes led to determination of the comet position that are less precise than what we can derive today by using a more modern star catalogue. Aims. We aim to provide a new catalogue of cometary orbits that are derived using a completely homogeneous data treatment, accurate numerical integration, and a modern model of the solar system. Methods. We collected the complete sets of observations for investigated comets from the original publications. Then we recalculated the cometary positions for the comet-minus-star-type of observations using the Positions and Proper Motions Star Catalogue, and applied a uniform method for the data selection and weighting. As a final result, new osculating orbits were determined. Secondly, dynamical calculations were performed to the distance of 250 AU from the Sun to derive original and future barycentric orbits for evolution backward and forward in time. These numerical calculations for a given object start from a swarm of virtual comets constructed using our osculating (nominal) orbit. In this way, we obtained the orbital element uncertainties of original and future barycentric orbits. Results. We present homogeneous sets of orbital elements for osculating, original, and future orbits for 38 one-apparition comets. Non-gravitational orbits are derived for thirteen of them.

Long-term orbital evolution of dust particles ejected from comet Encke

Abstract The 10,000 year long-term orbital evolution of six model dust particles ejected from the comet Encke at its perihelion has been investigated. Particles with ejection velocity 40 m s −1 were released in the following directions (two orientations for each direction): tangential to the cometary motion, normal to the comets orbital plane and perpendicular to the preceding ones. Planetary perturbations, excluding Pluto, and the simultaneous action of the Poynting-Robertson effect and the well-known form of the equation for the solar wind have been taken into account. Simulations have been done for dust particles of several sizes (0.1–1.5 cm). The obtained dispersions in orbital elements have been compared with the data observed.

Origin of the Taurid meteor stream

Abstract The origin of the Taurid meteor stream is investigated on the basis of the assumption that the complete set of observable quantities may be explained as a simultaneous action of nongravitational forces acting on meteoroids ejected from the parent body represented only by comet P\Encke. Discussion is concentrated on the problem of whether or not the assumption of the importance of nongravitational forces is acceptable. Numerical values for nongravitational acceleration are presented. A time evolution from 10,000 to 15,000 years is considered and graphically presented. The test is made for dust particles ejected at perihelia of the orbit of the comet Encke. The particles are released at velocities of 20–600 m s −1 . Gravitational perturbations of all planets and nongravitational effects are considered.

Orbital dispersion of comet Encke's meteoroids

The orbital evolution of model meteoroids ejected from the comet Encke has been investigated. The particles abandon the mother body with velocities 20 and 40 ms-1 perihelion within the interval of the past 10,000 years. Their 10,000 years old osculating orbits were numerically integrated forward, using a dynamical model of the solar system consisting of all planets. Forces from solar electromagnetic and corpuscular radiation effecting the particles are considered, too. Orbital dispersions of the model meteoroids are presented. The importance of nongravitational forces for a long-term orbital evolution of meteoroid streams is shown.

Orbital evolution of Jupiter's 8th satellite

Abstract The orbitai evolution of Pasiphae,the 8th satellite of Jupiter, has been investigated. Its osculating orbit for the epoch 29 October 1983 was numerically integrated over the interval of 20,000 years. Within the investigated time interval also the question of the Hills stability has been studied. The Jacobian constant, generalized to the avegaged elliptic problem. calculated from position and velocities obtained by numerical integration, changes less then the order of 10−8 The dominant pertubations by the Sun to the satellite allow us to use the intermediate orbit of the averaged elliptic three-body problem for investigation of the evolutionary change in the motion of the satellite. The mean motion of the agreement of perijove and the ascending node of the satellite are defined by analytical formulae, using the osculating non-Keplerian ellipse with moving node and perijove, and changing eccentricity. The results obtained according to this theory are comparable with those calculated from the numerical integration.

On the Importance of the Poynting-Robertson Effect on Meteoroids

A small generalization of the equation of motion for the Poynting-Robertson effect is tested in order to find the significance of new terms. The test is made for dust particles ejected at perihelia of the orbit of the comet Encke. The particles are released at the speed of 40 m s−1. Gravitational perturbations of planets, Poynting-Robertson effect and solar corpuscular radiation (solar wind) are considered. Other nongravitational effects may be represented by new terms in the suggested form of the nongravitational force. Various values of normal and transversal components of the perturbing nongravitational force are used. The final results of numerical integrations are compared with those obtained on the basis of the Poynting-Robertson effect.

An Extra-Solar Planet in a Double Stellar System: The Modelling of Insufficient Orbital Elements

The modelling of the insufficient orbital elements of extra-solar planets (EPs) re- volving around one component in a binary star system is investigated in the present paper. This problem is considered in the frame of the three-body problem using the analytical theory of Orlov & Solovaya (1998). In the general case, the motion is defined by the masses of the components and by the six pairs of the initial values of the Keplerian elements. For EPs, it is not possible to obtain the complete set of elements for the orbit, in particular, the ascending node and the angle of the inclination. So, it is possible the two different variants of orbital evolution of EPs depend on the initial conditions. In one case, the orbit is unstable. Using the stability conditions of Solovaya & Pittich (2004), which are presented by the angle of the mutual inclination of the orbits between the EP and distant star, we varied unknown angular elements and defined the regions with possible values of the elements for which the motion of EP stays stable. We applied these calculations to the particular specific EPs: HD19994b, HD196885Ab and HD222404b.

Application of the Nonrestricted Three-Bodies Problem to the Stellar System ξ UMa

The present study concerns the application of an analytical theory of the stellar three- - bodies problem to the triple stellar system ξ UMa, whose components move along short-period orbits with periods of 2 years and 60 years. For this purpose the solution of the simplified canonical system of differential equations obtained in terms of hyperelliptic integrals by Hamilton-Jacobi method was used. The precision of the solution was increased by addition of short-periodic terms computed from the formulae of the transformation by von Zeipel’s method.

Activity of the Lyrid meteor shower in the years 1945–1952

The activity of the Leonid shower in the years 1944–1953 was derived from visual records obtained at the Skalnate Pleso Observatory, using the zenithal exponent γ = 1.47 in the reduction factor cosγzR.

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.